CN105577194B - The fixed multi code Rate of Chinese character low-density check LDPC code building method of code length - Google Patents

The fixed multi code Rate of Chinese character low-density check LDPC code building method of code length Download PDF

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CN105577194B
CN105577194B CN201510970151.4A CN201510970151A CN105577194B CN 105577194 B CN105577194 B CN 105577194B CN 201510970151 A CN201510970151 A CN 201510970151A CN 105577194 B CN105577194 B CN 105577194B
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exposure mask
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CN105577194A (en
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白宝明
邱晨
穆锡金
陈刚
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Xidian University
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    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
    • H03M13/1148—Structural properties of the code parity-check or generator matrix
    • H03M13/1151—Algebraically constructed LDPC codes, e.g. LDPC codes derived from Euclidean geometries [EG-LDPC codes]

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Abstract

The invention discloses the multi code Rate of Chinese character low-density check LDPC code building methods that a kind of code length is fixed.Its scheme is: 1. according to the highest code rate R of the multi code Rate of Chinese character LDPC code to be constructed1Determine the columns N of recycle ratio Matrix C；2. choosing the prime P for being greater than columns N, and determine cyclic permutation matrices size L and code length n；3. constructing finite field according to prime P, the primitive element α chosen in finite field determines recycle ratio Matrix Ck；4. determining that R is equal to three different code rate R using optimization algorithmkLDPC code exposure mask matrix Bk；5. according to the recycle ratio Matrix C of each code ratekWith exposure mask matrix BkDetermine the basic matrix D of each code ratek；6. according to basic matrix DkDetermine the check matrix H of the LDPC code of each code ratek, finally obtain one group of check matrix of multi code Rate of Chinese character LDPC code.Compared with existing, the code length of the multi code Rate of Chinese character LDPC code of construction can fix, can directly be encoded with check matrix, be easy to hardware realization the present invention, can be used for satellite communication system and cellular communication.

Description

The fixed multi code Rate of Chinese character low-density check LDPC code building method of code length
Technical field
The invention belongs to wireless communication technology fields, more particularly to the multi code Rate of Chinese character low-density check that a kind of code length is fixed The building method of LDPC (Low-Density Parity-Check Codes) code, can be used for military channels, satellite communication The multi code Rate of Chinese character error control code of system and cellular communication system.
Background technique
In order to carry out reliable transmission in time-varying or noisy channel, the LDPC code of one group of code rate flexibility and changeability is needed, When channel condition is preferable, efficiency of transmission is improved using the code of high code rate；When channel condition is poor, low code is used The code of rate ensures transmission reliability.If the code of each code rate has different code lengths, will change in specific transmission Data grouping mode or transmission frame length, this will increase the overall complexity of communication system.For this problem, it has been proposed that The fixed multi code Rate of Chinese character code of code length, i.e., increase or decrease code rate under conditions of code length is fixed, to obtain the code of different code rates.
The method of the fixed multi code Rate of Chinese character LDPC code of construction code length is existed by scholars such as Andres I.Vila Casado earliest It is mentioned in " Multiple-Rate Low-Density Parity-Check Codes with Constant Blocklength " Row folding out constructs mother's LDPC code of a low bit- rate first, some check-nodes is then merged into a school Node is tested to obtain the code of high code rate, while certain sides in addition and deletion Turner figure are distributed raising property according to most goodness Can, but when the check matrix of the high code rate code of generation cannot merge or be discontented with the constraint of toe ring, need to regenerate low code Female code of rate, this makes yard construction process very complicated, or even cannot obtain one group of code for meeting all conditions.2011, The scholars such as Xueqin Jiang are in " Construction of Multiple-Rate Quasi-Cyclic LDPC Codes Using the multi-code that the row decomposition method construction code length based on hyperplane is fixed in via the Hyperplane Decomposing " Rate LDPC code is constructed mother's LDPC code of a high code rate first, is then decomposed into a check-node using algebraic method More check-nodes obtain the code of low bit- rate, but the obtained check matrix of this method does not have the knot for being easy and fast to coding Structure, this makes encoder complexity higher.
Summary of the invention
It is an object of the invention to propose a kind of multi code Rate of Chinese character LDPC code building method that code length is fixed, to overcome above-mentioned be based on Row merges or the deficiency of the multi code Rate of Chinese character LDPC code of row decomposition method construction.
The technical scheme is that constructing the irregular repeat accumulated code of a high code rate first as female code；Then Based on mother's code, code rate is reduced by reducing information bit simultaneously and increasing check bit；One group of code length is finally obtained to fix Multi code Rate of Chinese character LDPC code.Its realization includes the following steps:
1) according to the highest code rate R of the fixed multi code Rate of Chinese character LDPC code of the code length to be constructed1, determine recycle ratio Matrix C Columns:
2) prime P for being greater than columns N is chosen, and thereby determines that cyclic permutation matrices size L and code length n:
L=P-1, n=L × N
3) finite field gf (P) is constructed according to prime P, any primitive element α on the finite field gf (P) is chosen, different Code rate RkUnder, determine recycle ratio Matrix CkIn the i-th row jth column element valueK=1,2,3:
For 1≤i≤6, each element of 1≤j≤N-6, then
For 1≤i≤6, each element of N-5≤j≤N, then
For i=4, j=N-5, then
For 7≤i≤12, each element of 1≤j≤N-12, then
For 7≤i≤12, each element of N-11≤j≤N, then
For 13≤i≤18, each element of 1≤j≤N-18, then
For 13≤i≤18, each element of N-17≤j≤N, then
Wherein when code rate is R1When=(1-6/N), 1≤i≤6,1≤j≤N；When code rate is R2When=(1-12/N), 1≤i ≤ 12,1≤j≤N；When code rate is R3When=(1-18/N), 1≤i≤18,1≤j≤N；
4) the exposure mask matrix B of highest code rate LDPC code is determined1:
By columns N and code rate R1Set exposure mask matrix B1It is the matrix of 6 row N column, and determined according to density evolution theory B1Preceding N-6 column be by (N-6)/6 identical minor matrix BaIt arranges, last 6 column are the dual-diagonal matrixes of a tail biting Bb, that is:
Wherein,
5) determine that code rate is R2The exposure mask matrix B of the LDPC code of=(1-12/N)2:
5a) by the exposure mask matrix B of two highest code rate LDPC codes1By column to being spliced；
1 to 6 row, N-11 to the N-6 column in spliced matrix 5b) are become into full null matrix respectively；By 7 to 12 rows, N- 11 to N-6 column become single diagonal matrix；N-5, N-3 and N-1 column of 7 to 12 rows are become into full null vector；
Column minimum by the end of thresholding in 7 to 12 rows 5c) are selected using P-EXIT chart tool, and these column are become Full null vector is to get the exposure mask matrix B for arriving the LDPC code that code rate is (1-12/N)2；
6) determine that code rate is R3The exposure mask matrix B of the LDPC code of=(1-18/N)3:
6a) by the exposure mask matrix B of (1-12/N) code rate LDPC code2With the exposure mask matrix B of highest code rate LDPC code1By column to Spliced；
1 to 12 row, N-17 to the N-12 column in spliced matrix 6b) are become into full null matrix respectively；By 13 to 18 rows, N-17 to N-12 column become single diagonal matrix；13 to 18 rows, N-11 to N-6 column are become into full null matrix；By the N- of 13 to 18 rows 5, N-3 and N-1 column become full null vector；
Column minimum by the end of thresholding in 13 to 18 rows 6c) are selected using P-EXIT chart tool, and these column are become The exposure mask matrix B for the LDPC code that code rate is (1-18/N) is arrived for full null vector3；
7) according to each code rate RkCorresponding exposure mask BkDetermine the basic matrix D of each code ratek:
Assuming that recycle ratio Matrix CkThe element value of ith row and jth column beExposure mask matrix BkIth row and jth column Element value isThen basic matrix DkThe element of middle ith row and jth columnValue are as follows:
Basic matrix DkAre as follows:
8) according to each code rate RkBasic matrix DkDetermine the check matrix H for corresponding to the LDPC code of each code ratek:
IfThen check matrix Hk(L × (i-1)+1) to (L × i) it is capable and (L × (j-1)+1) to (L × j) It is classified as L rank full null matrix；
IfThen check matrix Hk(L × (i-1)+1) to (L × i) it is capable and (L × (j-1)+1) to (L × j) It is classified as L rank unit matrix cyclic shift to the rightThe obtained matrix in position；
In different code rate RkUnder obtain the identical one group of check matrix H of code lengthk。
Present invention incorporates the methods in LDPC code construction based on algebraical sum based on figure, can easily construct one group of code length Fixed multi code Rate of Chinese character LDPC code, and the multi code Rate of Chinese character LDPC code constructed can be used directly check matrix and carry out system coding, be easy to hard Part is realized, is had excellent performance.
Simulation result shows: the multi code Rate of Chinese character LDPC code constructed using the present invention is all with good performance in each code rate.
Detailed description of the invention
Fig. 1 is implementation flow chart of the invention；
Fig. 2 is the scatter plot of the check matrix H of 5/6 code rate LDPC code constructed with the embodiment of the present invention；
Fig. 3 is the scatter plot of the check matrix H of 2/3 code rate LDPC code constructed with the embodiment of the present invention；
Fig. 4 is the scatter plot of the check matrix H of 1/2 code rate LDPC code constructed with the embodiment of the present invention；
Fig. 5 is with performance simulation figure of the invention.
Specific embodiment
The building method and effect of the fixed multi code Rate of Chinese character LDPC code of code length of the present invention are described in detail with reference to the accompanying drawing.
The present invention is a kind of multi code Rate of Chinese character LDPC code building method that code length is fixed, is by exposure mask matrix B, recycle ratio square Battle array C, basic matrix D and L rank unit matrix construction.Multi code Rate of Chinese character is taken by element in designed mask matrix and recycle ratio matrix Value reduces information bit to the high code rate mother LDPC code of the function admirable constructed in advance while increasing check bit and realizes.
The present invention is with a length of 2376 bit of the fixed code of construction, and code rate R is respectively 5/6,2/3,1/2 multi code Rate of Chinese character LDPC It is described for code
Referring to Fig.1, steps are as follows for the realization of this example:
Step 1, according to the fixed multi code Rate of Chinese character LDPC code highest code rate R of the code length to be constructed1=5/6 determines recycle ratio square The columns N of battle array:
Step 2, prime P=67 for being greater than N=36 are chosen, and determine cyclic permutation matrices size L and code length n:
L=P-1=66,
N=L × N=66 × 36=2376 bit.
Step 3, each code rate R is determinedkUnder corresponding recycle ratio Matrix CkThe element value of middle ith row and jth columnIts Middle k=1,2,3, i ∈ { 1,2 ..., 18 }, j ∈ { 1,2 ..., 36 }:
The value of i and j is with code rate RkDifference and it is different: when code rate be R1When=5/6,1≤i≤6,1≤j≤36；When Code rate is R2When=2/3,1≤i≤12,1≤j≤36；When code rate is R3When=1/2,1≤i≤18,1≤j≤36；
Primitive element α=2 of finite field gf (67) are chosen, and are determined according to the primitive elementNumerical value, obtain code rate be R1 Recycle ratio Matrix C when=5/61Element it is as follows:
19 63 32 54 29 53 47 59 11 30 33 24 61 22 28 48 40 25 15 20 0 0 0 0 0 0
5 7 21 65 34 56 31 55 49 61 13 32 35 26 63 24 30 50 42 27 0 0 0 0 0 0
53 39 7 9 23 1 36 58 33 57 51 63 15 34 37 28 65 26 32 52 0 0 0 0 0 0
16 58 55 41 9 11 25 3 38 60 35 59 53 65 17 36 39 30 1 28 1 0 0 0 0 0
17 46 18 60 57 43 11 13 27 5 40 62 37 61 55 1 19 38 41 32 0 0 0 0 0 0
56 60 19 48 20 62 59 45 13 15 29 7 42 64 39 63 57 3 21 40 0 0 0 0 0 0
Obtaining code rate is R2Recycle ratio Matrix C when=2/32Element it is as follows:
19 63 32 54 29 53 47 59 11 30 33 24 61 22 28 48 40 25 15 20 0 0 0 0 0 0
5 7 21 65 34 56 31 55 49 61 13 32 35 26 63 24 30 50 42 27 0 0 0 0 0 0
53 39 7 9 23 1 36 58 33 57 51 63 15 34 37 28 65 26 32 52 0 0 0 0 0 0
16 58 55 41 9 11 25 3 38 60 35 59 53 65 17 36 39 30 1 28 1 0 0 0 0 0
17 46 18 60 57 43 11 13 27 5 40 62 37 61 55 1 19 38 41 32 0 0 0 0 0 0
56 60 19 48 20 62 59 45 13 15 29 7 42 64 39 63 57 3 21 40 0 0 0 0 0 0
10 43 58 62 21 50 22 64 61 47 15 17 31 9 0 0 0 0 0 0 0 0 0 0 0 0
26 13 12 45 60 64 23 52 24 0 63 49 17 19 0 0 0 0 0 0 0 0 0 0 0 0
39 5 28 15 14 47 62 0 25 54 26 2 65 51 0 0 0 0 0 0 0 0 0 0 0 0
36 62 41 7 30 17 16 49 64 2 27 56 28 4 0 0 0 0 0 0 0 0 0 0 0 0
54 61 38 64 43 9 32 19 18 51 0 4 29 58 0 0 0 0 0 0 0 0 0 0 0 0
18 1 56 63 40 0 45 11 34 21 20 53 2 6 0 0 0 0 0 0 0 0 0 0 0 0
Obtaining code rate is R3Recycle ratio Matrix C when=1/23Element it is as follows:
19 63 32 54 29 53 47 59 11 30 33 24 61 22 28 48 40 25 15 20 0 0 0 0 0 0
5 7 21 65 34 56 31 55 49 61 13 32 35 26 63 24 30 50 42 27 0 0 0 0 0 0
53 39 7 9 23 1 36 58 33 57 51 63 15 34 37 28 65 26 32 52 0 0 0 0 0 0
16 58 55 41 9 11 25 3 38 60 35 59 53 65 17 36 39 30 1 28 1 0 0 0 0 0
17 46 18 60 57 43 11 13 27 5 40 62 37 61 55 1 19 38 41 32 0 0 0 0 0 0
56 60 19 48 20 62 59 45 13 15 29 7 42 64 39 63 57 3 21 40 0 0 0 0 0 0
10 43 58 62 21 50 22 64 61 47 15 17 31 9 0 0 0 0 0 0 0 0 0 0 0 0
26 13 12 45 60 64 23 52 24 0 63 49 17 19 0 0 0 0 0 0 0 0 0 0 0 0
39 5 28 15 14 47 62 0 25 54 26 2 65 51 0 0 0 0 0 0 0 0 0 0 0 0
36 62 41 7 30 17 16 49 64 2 27 56 28 4 0 0 0 0 0 0 0 0 0 0 0 0
54 61 38 64 43 9 32 19 18 51 0 4 29 58 0 0 0 0 0 0 0 0 0 0 0 0
18 1 56 63 40 0 45 11 34 21 20 53 2 6 0 0 0 0 0 0 0 0 0 0 0 0
40 38 20 3 58 65 42 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 32 42 40 22 5 60 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
35 30 4 34 44 42 24 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 20 64 33 55 30 54 48 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
38 6 8 22 0 35 57 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
57 54 40 8 10 24 2 37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Step 4, determine that code rate is R1=5/6 yard of exposure mask matrix B1:
If exposure mask matrix B11 to 6 row, 1 to 30 column be to be made of 5 identical minor matrixs；Exposure mask matrix B11 to 6 Row, 31 to 36 column are made of the dual-diagonal matrix of a tail biting, obtained exposure mask matrix B1It is as follows:
Step 5, determine that code rate is R2The exposure mask matrix B of=2/3 LDPC code2:
5a) the exposure mask matrix B for the LDPC code for being 5/6 by two code rates1By column to being spliced；
1 to 6 row, 25 to 30 column in spliced matrix 5b) are become into full null matrix respectively；By 7 to 12 rows, 25 to 30 Column become single diagonal matrix；The column of the 31 of 7 to 12 rows, 33 and 35 are become into full null vector；
Column minimum by the end of thresholding in 7 to 12 rows 5c) are selected using P-EXIT chart tool, and these column are become Full null vector obtains the exposure mask matrix B for the LDPC code that code rate is 2/32It is as follows:
Step 6, determine that code rate is R3The exposure mask matrix B of=1/2 LDPC code3:
6a) the exposure mask matrix B for the LDPC code for being 2/3 by code rate2The exposure mask matrix B for the LDPC code for being 5/6 with code rate1By column To being spliced；
1 to 12 row, 19 to 24 column in spliced matrix 6b) are become into full null matrix respectively；By 13 to 18 rows, 19 to 24 column become single diagonal matrix；13 to 18 rows, 25 to 30 column are become into full null matrix；The 31 of 13 to 18 rows, 33 and 35 are arranged and are become For full null vector；
Column minimum by the end of thresholding in 13 to 18 rows 6c) are selected using P-EXIT chart tool, and these column are become For full null vector, the exposure mask matrix B for the LDPC code that code rate is 1/2 is obtained3It is as follows:
Step 7, according to the recycle ratio Matrix C of each code ratekWith exposure mask matrix BkDetermine the basic matrix D of each code ratek:
Assuming that recycle ratio Matrix CkThe element value of ith row and jth column beExposure mask matrix BkIth row and jth column Element value isThen basic matrix DkThe element of middle ith row and jth columnValue are as follows:
Basic matrix DkAre as follows:
When code rate is 5/6, the basic matrix D that size is 6 rows 36 column is obtained1Are as follows:
When code rate is 2/3, the basic matrix D that size is 12 rows 36 column is obtained2Are as follows:
When code rate is 1/2, the basic matrix D that size is 18 rows 36 column is obtained3Are as follows:
Step 8, according to each code rate RkBasic matrix DkDetermine the check matrix H for corresponding to the LDPC code of each code ratek:
IfThen check matrix Hk(L × (i-1)+1) to (L × i) it is capable and (L × (j-1)+1) to (L × j) It is classified as L rank full null matrix；
IfThen check matrix Hk(L × (i-1)+1) to (L × i) it is capable and (L × (j-1)+1) to (L × j) It is classified as L rank unit matrix cyclic shift to the rightThe obtained matrix in position；
In different code rate RkUnder obtain the identical one group of check matrix of code length.
Due to check matrix HkIt is very big, therefore be illustrated in the accompanying drawings, it is wherein the school of 5/6 code rate LDPC code shown in Fig. 2 Test matrix H1Scatterplot, be the check matrix H of 2/3 code rate LDPC code shown in Fig. 32Scatterplot, 1/2 code rate LDPC code shown in Fig. 4 Check matrix H3Scatterplot.Scatterplot position in every width figure indicates that the element value of check matrix is 1, and blank space indicates check matrix Element value be 0.
Effect of the invention can be further illustrated by following emulation:
The multi code Rate of Chinese character LDPC code progress BPSK modulation that the code length that 1. couples of present invention construct is fixed as 2376 bits is emulated, then is passed through Awgn channel is crossed, finally in receiving end use and product decoding algorithm, 50 progress bit error rate performance emulation of iteration, as a result such as Fig. 5 It is shown.
As seen from Figure 5, the LDPC code that the code length that the present invention constructs is fixed as 2376 bits has preferably under each code rate Performance.

Claims (3)

1. the fixed multi code Rate of Chinese character low-density check LDPC code building method of code length, be by recycle ratio Matrix C, exposure mask matrix B, Basic matrix D and L rank cyclic permutation unit matrix construction comprising following steps:
1) according to the highest code rate R of the fixed multi code Rate of Chinese character LDPC code of the code length to be constructed1, determine the column of recycle ratio Matrix C Number:
2) prime P for being greater than columns N is chosen, and thereby determines that cyclic permutation unit matrix size L and code length n:
L=P-1, n=L × N
3) finite field gf (P) is constructed according to prime P, any primitive element α on the finite field gf (P) is chosen, in different code rate Rk Under, determine recycle ratio Matrix CkIn the i-th row jth column element valueWherein k=1,2,3, i ∈ { 1,2 ..., 18 }, j ∈ The value of { 1,2 ..., 36 }, i and j are with code rate RkDifference and it is different: when code rate be R1When=(1-6/N), 1≤i≤6,1 ≤j≤36；When code rate is R2When=(1-12/N), 1≤i≤12,1≤j≤36；When code rate is R3When=(1-18/N), 1≤i≤ 18,1≤j≤36；
4) the exposure mask matrix B of highest code rate LDPC code is determined1:
By columns N and code rate R1Set exposure mask matrix B1It is the matrix of 6 row N column, and B is determined according to density evolution theory1's Preceding N-6 column are by (N-6)/6 identical minor matrix BaIt arranges, last 6 column are the dual-diagonal matrix B an of tail bitingb, that is:
Wherein,
5) determine that code rate is R2The exposure mask matrix B of the LDPC code of=(1-12/N)2:
5a) by the exposure mask matrix B of two highest code rate LDPC codes1By column to being spliced；
1 to 6 row, N-11 to the N-6 column in spliced matrix 5b) are become into full null matrix respectively；Extremely by 7 to 12 rows, N-11 N-6 column become single diagonal matrix；N-5, N-3 and N-1 column of 7 to 12 rows are become into full null vector；
Column minimum by the end of thresholding in 7 to 12 rows 5c) are selected using P-EXIT chart tool, and these column are become complete zero Vector is to get the exposure mask matrix B to code rate for the LDPC code of (1-12/N)2；
6) determine that code rate is R3The exposure mask matrix B of the LDPC code of=(1-18/N)3:
6a) by the exposure mask matrix B of (1-12/N) code rate LDPC code2With the exposure mask matrix B of highest code rate LDPC code1By column to progress Splicing；
1 to 12 row, N-17 to the N-12 column in spliced matrix 6b) are become into full null matrix respectively；By 13 to 18 rows, N-17 Become single diagonal matrix to N-12 column；13 to 18 rows, N-11 to N-6 column are become into full null matrix；By N-5, N-3 of 13 to 18 rows Become full null vector with N-1 column；
Column minimum by the end of thresholding in 13 to 18 rows 6c) are selected using P-EXIT chart tool, and these column are become complete Null vector is to get the exposure mask matrix B to code rate for the LDPC code of (1-18/N)3；
7) according to each code rate RkCorresponding exposure mask BkDetermine the basic matrix D of each code ratek:
Assuming that recycle ratio Matrix CkThe element value of ith row and jth column beExposure mask matrix BkThe element of ith row and jth column Value isThen basic matrix DkThe element of middle ith row and jth columnValue are as follows:
Basic matrix DkAre as follows:
8) according to each code rate RkBasic matrix DkDetermine the check matrix H for corresponding to the LDPC code of each code ratek:
IfThen check matrix Hk(L × (i-1)+1) to (L × i) it is capable and (L × (j-1)+1) to (L × j) is classified as L Rank full null matrix；
IfThen check matrix Hk(L × (i-1)+1) to (L × i) it is capable and (L × (j-1)+1) to (L × j) is classified as L Rank unit matrix cyclic shift to the rightThe obtained matrix in position；
In different code rate RkUnder obtain the identical one group of check matrix H of code lengthk。
2. according to the method described in claim 1, it is characterized by: the recycle ratio Matrix C determined in step 3)kIn the i-th row The element value of j columnIt is to be determined according to the value of different i and j:
For 1≤i≤6, each element of 1≤j≤N-6, then
For 1≤i≤6, each element of N-5≤j≤N, then
For i=4, j=N-5, then
For 7≤i≤12, each element of 1≤j≤N-12, then
For 7≤i≤12, each element of N-11≤j≤N, then
For 13≤i≤18, each element of 1≤j≤N-18, then
For 13≤i≤18, each element of N-17≤j≤N, then
3. according to the method described in claim 1, it is characterized by: in step 2) cyclic permutation unit matrix size L and code length n with The difference of prime P that is selected and change, to realize the variable characteristic of code length.
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